Page 56 - Introduction to Naval Architecture

FLOTATION AND STABILITY 43

which would be WX GM L/100L. In Imperial units the moment to change
trim one inch is usually quoted. In this latter case the units must be
watched. If Wis in tonft and L and GM L are in feet then:

The value of MCT is very useful in calculating the draughts at which a
ship will float for a given condition of loading. Suppose it has been
ascertained that the weight of the ship is Wand the centre of gravity is x
forward of amidships and that at that weight with a waterline parallel to
the design waterline it would float at a draught T with the centre of
buoyancy^ forward of amidships. There will be a moment W(y-x) /MCT
taking it away from a waterline parallel to the design one. The ship trims
about the centre of flotation and the draughts at any point along the
length can be found by simple ratios.

Example 4.1
A ship of mass 5000 tonnes, 98m long, floats at draughts of 5.5 m
forward and 6.2 m aft, being measured at the extreme ends. The
longitudinal metacentric height is 104m and the centre of
flotation is 2.1m aft of amidships. Determine the moment to
change trim 1 cm and the new end draughts when a mass of 85
tonnes, which is already on board, is moved 30 m forward.

Solution

As the mass is already on board there will be no bodily sinkage.
The change of trim is given by the trimming moment divided by
MCT.